广西师范大学学报（自然科学版） ›› 2017, Vol. 35 ›› Issue (2): 39-44.doi: 10.16088/j.issn.1001-6600.2017.02.006

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二维典型群PSL(2,q)与旗传递2-(v, k, λ)设计

王培, 周胜林*   

  1. 华南理工大学数学学院,广东广州510640
  • 出版日期:2017-07-25 发布日期:2018-07-25
  • 通讯作者: 周胜林(1968—),男, 湖北罗田人,华南理工大学教授,博士。E-mail:slzhou@scut.edu.cn
  • 基金资助:
    国家自然科学基金(11471123)

Two Dimensional Classical Groups PSL(2,q)and Flag-transitive 2-(v,k,λ) Designs

WANG Pei, ZHOU Shenglin*   

  1. School of Mathematics, South China University of Technology, Guangzhou Guangdong 510640, China
  • Online:2017-07-25 Published:2018-07-25

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摘要： 旗传递性是附加在2-设计的自同构群上的重要条件之一。1988年,Zieschang证明了旗传递2-(v,k,λ)设计当(r,λ)=1时其自同构群G只能是仿射群或者几乎单群,故可以利用有限单群分类定理来分类此类设计。本文研究自同构群G是旗传递的且其基柱Soc(G) 为单群PSL(2,q) 的2-(v,k,λ) 设计,解决了在限制条件(r,λ)=1且v≤1 000 时此类设计的分类问题, 共存在18个两两不同构的设计。

关键词: 2-设计, 旗传递, 点本原, 基柱, 二维典型群

Abstract: Flag-transitivity is one of the many conditions that can be imposed on the automorphism group G of a 2-(v,k,λ) design D. In 1988, it is proved by Zieschang that if D is a 2-(v,k,λ) design, G≤Aut(G) is flag-transitive and (r,λ)=1, then G is affine or almost simple. So it is possible to classify this type of designs by using the classification of finite simple groups. Let D be a nontrivial 2-(v,k,λ) design with (r,λ)=1 and v≤1 000, and let G≤Aut(D) be flag-transitive with Soc(G)PSL(2,q). It is proved that, up to isomorphism, there are exactly 18 pairs (D, G).

Key words: 2-design, flag-transitive, point-primitive, socle, two dimensional classical groups

中图分类号: 

  • O152.1
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